For each of the six diagrams replace the forces with an equivalent force-couple system at A. Note which, if any, systems are equivalent 5 in. 3 lb 2 lb 3 in. 2 lb 4 lb 6 lb- in. (а) (b) (c)

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**Educational Content: Force-Couple Systems**

The image depicts six diagrams illustrating force systems acting on rectangular boxes. Each diagram has forces applied at different points, which should be replaced with an equivalent force-couple system at point A. The task is also to identify if any of these force systems are equivalent.

### Diagrams:

#### Diagram (a)
- **Forces:**
  - A 6 lb force acts upward along the z-axis.
  - A 2 lb force acts downward parallel to the y-axis.
- **Dimensions:**
  - The z-axis force is 5 inches from point A, and the y-axis force is 3 inches from A.

#### Diagram (b)
- **Forces:**
  - A 6 lb force acts upward aligned with the z-axis.
  - A 3 lb force acts leftward along the y-axis.
  - A 4 lb force acts downward parallel to the x-axis.

#### Diagram (c)
- **Forces:**
  - A 6 lb force acts upward along the z-axis.
  - A 2 lb force acts downward and diagonally pointing towards the positive x and negative y directions.
- **Dimensions:**
  - The diagonal force is 6 inches from the z-axis.

#### Diagram (d)
- **Forces:**
  - A 3 lb force acts upward parallel to the z-axis.
  - A 3 lb force acts leftward parallel to the y-axis.
  - A 3 lb force acts forward along the x-axis.
- **Dimensions:**
  - A 13 lb force is directed away from the box diagonally from point A.

#### Diagram (e)
- **Forces:**
  - A 2 lb force acts upward along the positive z-axis.
  - A 1 lb force acts inward towards the front of the box on the x-axis.
  - A 3 lb force acting downward parallel to the z-axis.

#### Diagram (f)
- **Forces:**
  - A 9 lb force acts upward along the z-axis.
  - A 25 lb diagonal force acts downward and extends both along the positive y and negative x directions.
- **Dimensions:**
  - The diagonal force is positioned 5 inches from the front face of the box.
  - The vertical force is 4 inches away from A.
  - The diagonal force is 16 inches away from A.

### Objective:
For each
Transcribed Image Text:**Educational Content: Force-Couple Systems** The image depicts six diagrams illustrating force systems acting on rectangular boxes. Each diagram has forces applied at different points, which should be replaced with an equivalent force-couple system at point A. The task is also to identify if any of these force systems are equivalent. ### Diagrams: #### Diagram (a) - **Forces:** - A 6 lb force acts upward along the z-axis. - A 2 lb force acts downward parallel to the y-axis. - **Dimensions:** - The z-axis force is 5 inches from point A, and the y-axis force is 3 inches from A. #### Diagram (b) - **Forces:** - A 6 lb force acts upward aligned with the z-axis. - A 3 lb force acts leftward along the y-axis. - A 4 lb force acts downward parallel to the x-axis. #### Diagram (c) - **Forces:** - A 6 lb force acts upward along the z-axis. - A 2 lb force acts downward and diagonally pointing towards the positive x and negative y directions. - **Dimensions:** - The diagonal force is 6 inches from the z-axis. #### Diagram (d) - **Forces:** - A 3 lb force acts upward parallel to the z-axis. - A 3 lb force acts leftward parallel to the y-axis. - A 3 lb force acts forward along the x-axis. - **Dimensions:** - A 13 lb force is directed away from the box diagonally from point A. #### Diagram (e) - **Forces:** - A 2 lb force acts upward along the positive z-axis. - A 1 lb force acts inward towards the front of the box on the x-axis. - A 3 lb force acting downward parallel to the z-axis. #### Diagram (f) - **Forces:** - A 9 lb force acts upward along the z-axis. - A 25 lb diagonal force acts downward and extends both along the positive y and negative x directions. - **Dimensions:** - The diagonal force is positioned 5 inches from the front face of the box. - The vertical force is 4 inches away from A. - The diagonal force is 16 inches away from A. ### Objective: For each
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